Algorithm and hardware design of a 2D sorter-based K-best MIMO decoder

Tran et al. EURASIP Journal on Wireless Communications and Networking 2014, 2014:93 http://jwcn.eurasipjournals.com/content/2014/1/93 R ESEA R CH Open Access Algorithm and hardware design of a 2D sorter-based K-best MIMO decoder Thi Hong Tran1* , Yuhei Nagao2 and Hiroshi Ochi1 Abstract In the field of multiple input multiple output (MIMO) decoder, K-best has been well investigated because it guarantees an SNR-independent fixed-throughput with a performance close to the optimal maximum likelihood detection (MLD). However, the complexity of its expansion and sorting tasks is significantly affected by the constellation size W. In this paper, we propose an algorithm and hardware design of a 2D sorter-based K-best MIMO decoder whose complexity is negligibly affected by W. The main novelties of the algorithm are the following: (1) Direct expansion and parent node grouping ideas are proposed for reducing the expansion task’s complexity. (2) Two-dimensional (2D) sorter is proposed for simplifying the sorting task. The hardware design of the decoder supports up to 256-QAM modulation, which aims to apply into 4 × 4 MIMO 802.11n and 11ac systems. The paper shows that the proposed decoder outperforms the Bell Labs layered space-time (BLAST) minimum mean square error (MMSE) and lattice-reduction aided (LRA) MMSE, and is close to the full K-best in terms of bit error rate (BER) performance. The hardware design of the decoder is synthesized in application specific integrated circuit (ASIC) and compared with the previous works. As a result, it achieves the highest throughput (up to 2.7 Gbps), consumes the least power (56 mW), obtains the best hardware efficiency (15.2 Mbps/Kgate), and has the shortest latency (0.07 μs). Keywords: Maximum likelihood detection (MLD); K-best; MIMO decoder; IEEE 802.11n/ac; 256-QAM 1 Introduction Multiple input multiple output (MIMO) technology has shown a great promise for the future wireless communication because of its high spectral efficiency. For example, it has been applied in many wireless communication standards such as IEEE 802.16 e/m and IEEE 802.11 n/ac [1]. As an important part of the MIMO system, the MIMO decoder has been well investigated recently. Several types, such as maximum likelihood detection (MLD), linear minimum mean square error (LMMSE), Bell Labs layered space-time MMSE (BLAST MMSE), and lattice-reduction aided MMSE (LRA MMSE), have been proposed. Among these, it is well known that the MLD is the optimal approach in terms of bit error rate (BER) performance. However, its complexity increases exponentially with the number of constellation points of the modulation and with the number of spatial streams [2]. Several researches on suboptimal MLD algorithms, especially on the full *Correspondence: 1 Kyushu Institute of Technology, 680-4 Kawazu Iizuka, Fukuoka 820-8502, Japan Full list of author information is available at the end of the article K-best, have been done instead. If a MIMO system sends data via N spatial streams, the full K-best will process through N stages. In each stage, it firstly computes the Euclidean distance from the received information to all of the constellation nodes (i.e., expansion task) and then sorts the obtained results (i.e., sorting task) to select K best nodes. If we denote W as the number of constellation nodes, complexity of the expansion and sorting tasks increases proportionally to W and W 2 , respectively. To reduce the K-best’s complexity, several researches were carried out and published already. These researches can be classified into two methods named as complex domain and real domain. The former one processes through N stages as the full K-best does. However, new ideas are proposed to reduce the complexity in trade-off with an acceptable performance degradation. Some typical proposals on this method are a fixed sphere decoder algorithm - FSD in [3], a step reduced K-best sphere decoder algorithm in [4], and a zigzag on-demand expansion scheme in [5]. On the other hand, the real domain method separates the in-phase (IP) and quadrature-phase (QP) components of a complex data into two independent © 2014 Tran et al.; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. Tran et al. EURASIP Journal on Wireless Communications and Networking 2014, 2014:93 http://jwcn.eurasipjournals.com/content/2014/1/93 real data and processes these data in real domain. Thus, the complexity of each stage is reduced, while the number of stages is increased from N (in complex domain) to 2N (in real domain). The well-known researches on this method are [6-9]. Studying these proposals, we recognize that the expansion and sorting tasks are still too complex for practical implementation if a large value of K and high-order modulation types such as 256-QAM are needed. In this paper, we propose an algorithm and hardware design of a low complexity 2D sorter-based K-best MIMO decoder. The proposal bases on the complex domain method. The contributions of this paper is briefly described as follows: • In terms of algorithm, we propose direct expansion and parent node grouping methods to reduce the expansion’s complexity, and two dimensional (2D) sorter to simplify the sorting task. The direct expansion specifies the best candidates directly without searching all the constellation nodes. Consequently, complexity of the algorithm is negligibly affected by constellation size. The Euclidean distance computation becomes simpler, and the divider is eliminated. The parent node grouping helps to reduce the number of search candidates within an acceptable amount without trade-off of the BER performance. The 2D sorter does the matrix-based sorting. It has low complexity, is suitable for hardware resource sharing, and provides approximate result. • In terms of hardware architecture, a prototype of the algorithm which aims to support 4 × 4 MIMO 802.11n/ac systems is developed. We utilize some techniques such as resource sharing and GAIN-MUX-based multiplier to further reduce the complexity. The rest of this paper is organized as follows: Section 2 shows the preliminary information such as notations, channel model, and full K-best algorithm. Section 3 describes our algorithm. Section 4 focuses on hardware design. Sections 5 and 6 compare the proposed one with the previous works in terms of BER performance and application specific integrated circuit (ASIC) results, respectively. We conclude the paper in Section 7. 2 Background 2.1 Notations We shall use bold lowercase letters for vectors and bold capital letters for matrices. Furthermore, ·  denotes the L − 2 norm distance or Euclidean distance, (· )H denotes the Hermitian transpose of a matrix, and (· )I and (· )Q respectively denote the i (...truncated)